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A Novel Technique to Design and Optimize Performances of Custom Load Cells for Sport Gesture Analysis
IRBM 40 (2019) 201–210
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IRBM www.elsevier.com/locate/irbm
HEALTHCOM 2018
A Novel Technique to Design and Optimize Performances of Custom Load Cells for Sport Gesture Analysis D. Bibbo a,∗ , S. Gabriele b , A. Scorza a , M. Schmid a , S.A. Sciuto a , S. Conforto a a b
Department of Engineering, Roma Tre University, Rome, Italy Department of Architecture, Roma Tre University, Rome, Italy
h i g h l i g h t s
g r a p h i c a l
a b s t r a c t
• In cycling, estimation of exerted force through force sensors requires high accuracy. • Design of the sensor placement on the pedal can profit from FEM analysis. • Parametric strain-load curves give sensitivity to force and position dependence. • Optimal placement: trade-off between sensitivity and dependence to position changes.
a r t i c l e
i n f o
Article history: Received 13 December 2018 Received in revised form 6 May 2019 Accepted 21 May 2019 Available online 4 June 2019 Keywords: Dynamic analysis Load cells Strain gauges FEM analysis Cycling
a b s t r a c t Background: The assessment of the force exerted during a gesture in human motion analysis can provide direct and indirect information regarding the expended energy, especially during the execution of a sport gesture. In this field, assessment and improvement of the performance can be supported by instrumented devices able to measure and process mechanical quantities. In cycling, strain gauges-based instrumented pedals represent one of the last innovations in the sector, because they can provide data about the power exerted (produced) during training and the pedal efficiency. Optimization of the strain-gauges positioning is thus required to improve accuracy in the exerted force estimation. Methods: A new technique to give a support for evaluating the best compromise between maximum sensitivity and ease of assembly was developed in the present work, based on a Finite Element Model (FEM) and a parametric analysis of the strain field at different sensor placements. Optimal positions were identified as those combining high sensitivity and low dependence from positioning inaccuracies. Results: Parametric strain-load trends obtained from the developed model show a linear behavior of strain gauges pairs and confirm that there is a good sensitivity of the adopted sensors if they are mounted in handy positions of the developed load cell. Discussion: The conducted analysis enables to calculate the sensitivity of the load cell to the exerted forces, and evaluates its dependence to the positioning of strain gauges, and makes it possible to appropriately choose strain gauges positioning in areas where border effects are minimized. The strain distributions obtained by the FEM analysis in the presented load cells gives useful indications for all the situations where small strain gauges are requested to be mounted on a reduced offered area. © 2019 AGBM. Published by Elsevier Masson SAS. All rights reserved.
1. Introduction
*
Corresponding author. E-mail address: [email protected] (D. Bibbo).
https://doi.org/10.1016/j.irbm.2019.05.005 1959-0318/© 2019 AGBM. Published by Elsevier Masson SAS. All rights reserved.
Sport science in the last decades has taken great advantage from the use of electronic devices dedicated both to athletes’ ges-
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ture monitoring and to the provision of real-time feedback information, with the aim of improving performance. The information obtained by measuring human motion parameters can be used to assess the correct execution of motor tasks that compose the gesture itself or to recognize dynamic activities [1–5]. One of the main classifications of a sport gesture describes it as either an “open skill” sport discipline, characterized by a free and unconstrained strategy expressed by the athlete according to the specific situation (i.e. football, basket etc.), or as a “closed skill” one, characterized by the repetition as accurate as possible of a well-known gesture and by its almost automatic execution [6], such as in rowing, archery or cycling. In cycling the athlete continuously repeats the act of pedaling that implies a dynamic interaction with the pedal and can be well identified, quantified and interpreted. In general, the study of the cycling biomechanics can help to evaluate how the athlete executes the required motor task, especially when the performance can be assessed on the basis of objective parameters [7,8]. One of the most reliable methodologies widely used in this context is the pedaling power evaluation: this quantity can be assessed using different techniques [9], or on the basis of the estimation the muscle activity during the task [10]. During cycling, many factors contribute to the total resistance that must be overcome for the advancement of the bicycle, such as aerodynamic ones, mechanical frictions or rolling resistances, that can be equivalently schematized as a total resistant torque applied to the wheel. At constant pedaling, the forces applied to the pedal must win this resistant torque, thus the analysis of pedaling dynamics can give important information on the way such forces are applied and on their intensity. One important application of pedal use, described in some literature works, consists of the measurement of the external forces exerted on the pedal for predicting muscle force patterns, using an inverse dynamics approach [11,12]. Some of the most important proposals of the last decades are based on the measure of the forces applied to the pedal, using custom developed instrumented bicycle pedals. These solutions, useful to provide the dynamic information related to the foot-pedal interaction, are based on various technologies, aiming to obtain good performances in terms of accuracy and reliability. Soden and co-workers, in 1979 [13], presented one of the first proposals that demonstrated the feasibility of using such pedals. The main goal of the work was to obtain a tool for the design and the structural dimensioning of the bicycle frames. In doing this, authors proved, with a relative compact instrument, the possibility of measuring forces applied to the pedal, using different channels for each component of the dynamic measurement. After this, successive studies dealt with the development of a multicomponent instrumented pedal to measure kinetics (i.e. the threedimensional force and torque vectors in a reference system fixed to the pedal) and kinematics (i.e. the angle between the crank and the pedal) during cycling. It was assessed and demonstrated that to completely describe the cycling biomechanics these measurements were necessary, also for the calculation of the pedaling effective force [14,15], that causes bicycle progression. Successive works enlarged the knowledge on the pedaling technique [16,17] even if the described solutions were not useful for applications out of the laboratory environment. The first solution to overcome the described limits was proposed in 1998 [18] for off-road bicycles. A new instrumented pedal with dimensions and weight closer to a normal one, and so compatible with in-field applications, was presented, even if with some limitations. The acquisition system was compact and the load cell well designed, so allowing accurate measurements of the force components in agreement with the authors’ original aim relating to the stress analysis of the bicycle frame. This solution was affected by a pair of drawbacks preventing the transformation of this proposal into a com-
mercial device: i) wired connection of the instrumented pedal to the acquisition system; ii) crank modified to fit the instrumented pedal. Also, more recent proposals [19] imply non-negligible modifications on the bike, thus affecting the gesture execution. To be consistent with the original crankset geometry, the crank has to be shortened, thus the measuring device is not compliant with standard cranksets and can be used only in combination with tools providing different crank lengths. In the last years, among the commercial devices useful to evaluate the power exerted while pedaling, the Powermeter (SRM GMBH, Germany, EU) was introduced. Even if it represented a small revolution among sports bicycle users, it presents a main limit: this system provides only the resultant torque from which it is not possible to obtain the two contributions that each leg provides during cycling. To overcome these limits, a new system for torque and force measurements, based on a different general concept, was designed and developed by our group [20,21]. The design of such a system considers a new concept for the instrumented pedal body as well as its manufacturing process. One of the most important aspects in the design and realization of this system is the optimization of sensors dimensioning and placement, aiming to obtain the best tradeoff between bending behavior in the elastic field, that is related to the instrument sensitivity, and mechanical resistance. To this aim, and on the basis of a previous study by our group [22], in this paper a simulation of the strain field for different sensors positions was conducted. The results of this study can help support the evaluations of such kind of sensors design in order to achieve the best compromise between ease of assembly and maximum sensitivity. To this aim, after some theoretical considerations on sensors settings and configuration, numerical results from a 3D Finite Element Model (FEM) simulation are shown and discussed. The innovation consists also in a multi parametric 3D modelling and analysis, in which it is possible to variate the dimension of the load cell and of the strain gauges, together with the different positioning of those on the designed structure. The proposed method can be easily applied to a wide range of force sensors, especially the ones where the available area to fix sensors is reduced and strain gauges adopted are very small. The choice of an optimal position can guarantee a reduction of mounting errors, thus increasing the quality of the final product. 2. Materials and methods 2.1. Instrumented pedal mechanical design In order to reconstruct the effective component of force applied by the cyclist, which is the one orthogonal to the crank [16] and gives the necessary torque to move the bicycle, a novel instrumented pedal was designed. To this aim the necessary requirements are the possibility of measuring the three components of the force and the angle between the pedal and the pedal crank. Since in cycling even minimal variations to each bicycle component can affect the athlete’s performance, the pedal was designed with mechanical and geometrical features to be compliant, in terms of shape, weight and dimensions, to a commercial one. The pedal body, aiming at both weight and size optimization, was proposed and realized in a single block of aluminum alloy, and its weight, including all the complementary accessories, is 200 g. The shape allows a simple die-casting production because it does not present undercuts in its mechanical design. Moreover, the pedal body has some specific sensitive areas whose deformation can be associated with the load applied to the pedal by a cycling shoe commercial cleat. The central axis of the pedal used for the connection
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Fig. 1. Body of the designed instrumented pedal.
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Fig. 3. Effect on the lower parts of the 4 “L shape” elements while a Fz components is applied to the pedal. Sensitive areas 1 to 4 are highlighted.
Fig. 2. “L-shape” elements for the strain gauges fixing. The different sets are positioned in yellow, green and red highlighted areas for the measure of Fx, Fy and Fz respectively. Two yellow and green areas are not visible but located symmetrically to the visible ones with respect to the yz and xz planes. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.) Fig. 4. Strain gauge positioning for the Fz component measurement.
with the crank, as well as the spring mechanism for the cleat retain system, was taken from a commercial pedal solution (Shimano SPD-SL). The electronic circuits for conditioning, acquiring and transmitting signals from the force sensors are enclosed in a specific carter fixed to the pedal body. In the pedal design, shown in Fig. 1, the main concept has been to transmit the force flow from the shoes contact point to the crank via four sensitive and sensorized elements: the force exerted by the cyclist is applied on the upper load plate (1) that is fixed to the two lateral zones of the pedal body (2). Then the force is transmitted on four “L-shape” elements (3) on which the strain gauges are placed (see also Fig. 2). With reference to Fig. 1, these elements are connected to a central housing (4) in which the pedal shaft (along y axis), that connects the pedal to the crank, is fixed using bearings. It is important to highlight that elements 1 and 4 are not in contact so the force flow is transmitted only via the elements 3. On the opposite side of the threaded axis, a digital encoder is positioned (5), to measure the pedal-crank angle. The innovative pedal design therefore allows measuring the desired components presenting a compact and light shape and simplifies its manufacturing process. 2.2. Strain gauge disposition and assembly Under the action of a force applied on the pedal load plane, the “L shape” elements are deformed, under the hypothesis of an elastic behavior, in order to transduce the stress in strain. Consequently, the force effect that can be measured comes from a deformation of these elements, in different directions and intensity depending on the force components, schematized along the 3 axes (x, y, z) represented in Fig. 1. To evaluate deformations while applying force, 3 different sets of strain gauges (8 for each component, 24 total) are necessary to monitor the deformation of the “L-shape” elements, and are placed as shown in Fig. 2. Each set is assumed to measure the same kind of deformation, because the 3 force components act as a shear force on different parts of the “L-shape” element. These assumptions allow measuring the three components minimizing the cross
talk between channels: for example, considering the strain gauges set used to monitor the Fz component, this channel will have a zero output when Fx and Fy are applied on the load plane. The single strain gauge electrical resistance is in general proportional to its deformation, so the force applied to the pedal can be measured by assembling strain gauges in Wheatstone bridge configurations. In this way it is possible to assume that F = A × V out , with F representing the applied force, V out the bridge voltage output and A the coefficient that gives the linear proportionality. In this application three different sets of strain gauges are used to measure the three force components along the respective orthogonal axes. These sets are consequently assembled in 3 independent Wheatstone bridge circuits. The Fx, Fy and Fz force components can be obtained considering the superposition principle on each of the “L-shape” pedal elements: every part of each element, under the action of a single force component, has a behavior similar to a beam structure subject to a shear force. For example, when the Fz component is applied to the pedal, the situation can be considered equivalent as four components (Fz1 , Fz2 , Fz3 , Fz4 ), whose sum gives Fz, are applied to the lower parts of the 4 “L shape” elements (Fig. 3). The resulting deformation, as a first approximation, results as a consequence of the bending action of each (Fz1 , Fz2 , Fz3 , Fz4 ) component only. In this condition, a simplified model can be used to describe how to measure each Fzn shear component: the single element can be considered as a fixed beam, 2 strain gauges can be mounted in the external position “e” and internal position “i”, as shown in Fig. 4, to measure the resulting normal stresses. To do this, at first it is necessary to assume a linear elastic behavior of the material: under these conditions the stress/strain relation is given M by the σ = E ε = Wb . In a generic beam section, the deformation is consequently function of the force F , according to the equations:
ε=
Mb EW
where:
=F
1 EW
a
(1)
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Fig. 5. Wheatstone bridge configuration for the Fz component measurement.
• • • •
M b : the bending moment in the generic section n; a: the force arm; E: the Young’s modulus of the material; W : the modulus of the resistance to the bending.
Considering a pair of strain gauges “e” and “i” placed on one of the sensing elements (Fig. 4), with respective electrical resistance R e and R i and assembled in a Wheatstone bridge configuration (Fig. 5), the output signal is:
V out V in V out V in
=k =
Re Re
kG EW
−
Ri
Ri
= kG (εe − εi ) =
kG EW
(ae − ai ) F
dF
(2)
where:
• G: the Gauge Factor; • d: distance between the strain gauges; • k: constant of proportionality.
Fig. 6. 3D Geometry with a) loaded plates and b) restrained internal surface highlighted.
With this configuration, the measure of F is theoretically independent from its application point on the beam. Of course, this specific aspect is sensitive to the boundary conditions. On the basis of these considerations, 8 strain gauges can be fixed on the lowest part of the pedal as shown in Fig. 4 and assembled as shown in Fig. 5. As initial hypothesis a pair consists of a single matrix composed by 2 strain gauges, whose size is 1.5 × 1 mm. The 2 strain gauges are distant 0.5 mm so the matrix dimensions are 3.5 × 1 mm. Considering a V in input, the voltage output V out of the circuit is given by:
V out V in
=k +
1 Z e 1 Ze
4 Z e 4 Ze
−
1 Z i
−
4 Z i
1 Zi 4 Zi
+
2 Z e 2 Ze
−
2 Z i 2 Zi
+
3 Z e 3 Ze
−
3 Z i 3 Zi (3)
with {1Ze, 1Zi, 2Ze, 2Zi, 3Ze, 3Zi, 4Ze, 4Zi} the strain gauges electric resistance values and {1Ze, 1Zi, 2Ze, 2Zi, 3Ze, 3Zi, 4Ze, 4Zi} their variations, while Fz is applied and k a constant. The other two force components Fx and Fy can be measured in an equivalent way, so the analysis conducted in this paper for one of the components (Fz) can be repeated in the same way for the others. 2.3. Structural analysis To evaluate the strain values, in particular those close to the zones interested by the strain gauges position, a parametric mechanical analysis of the pedal was conducted. From a quantitative point of view, the analysis gives an estimation of the maximum strains experienced by the pedal and allows for verifying the consistency with the strain gauges sensitivities. Moreover, parametric
calculations help to infer the optimal positioning of the necessary sensors. A 3D FEM of the pedal has been implemented using COMSOL Multiphysics. In Fig. 6 the geometry of the model is shown, where the loaded plates (see also zones 2, Fig. 1) are highlighted. The pedal positioning with respect to the foot position during cycling can be simulated in the best way also considering some boundary conditions (BCs), given in half of the inner hollow surface of the pedal (see Fig. 6b). In this analysis the foot pressure is assumed normal to the loaded plates along the Z axis (Fig. 6a). All the geometrical details led to a very complex 3D mesh with a high number of edges: the complete mesh is depicted in Fig. 7 and consists of 32851 domain elements, 10390 boundary elements, and 2002 edge elements, the total number of degrees of freedom solved for is 154788. The provided numbers give an idea of the model complexity. In particular the domain elements are, in this case, tetrahedral objects where a physical problem to be solved can be attached. In the present case the linear static equilibrium equations are solved over the 3D domain ,
di v (S) = 0 in , S · n = f s on L , u = u on R
(4)
where S is the Cauchy stress tensor, f s are the surface loads applied on L and u are the values of the displacement boundary conditions applied on R . The strain gauges are simulated considering that the total strain of the sensor acts as the underneath surface, so the behavior can be considered to be the same. With these considerations, strain gauges can be simulated on the model as a pair of 2D rectangular patches, as in Fig. 7. To simulate their deformation an average operator is then applied to each of the patches, thus giving the mean value of the strain measure ε22 through the longest side of the patch. A proper fine meshing of the area around the patches (see
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Fig. 7. 3D mesh and strain gauge position simulation.
Fig. 8. Strain gauge positioning along vertical (y) and horizontal (x) directions. Positions are expressed in mm.
Fig. 7) is applied in order to improve the accuracy in the calculated average value of the strain. 2.4. Parametric technique for the strain gauge position analysis A parametric analysis has been conducted to study the position of the strain gauges. From a “zero” initial position that is depicted in Fig. 8, both translations along the vertical (y) and horizontal (x) directions are applied, as to obtain a matrix of 8 by 5 different strain gauges positions. The vectors of the translation parameters yp and xp, for the vertical and the horizontal positions respectively, are given in the following:
yp = {−0.5, 0, 1, 2, 3, 4, 5, 6} [mm] xp = {−2, −1, 0, 1, 2} [mm] Two different load conditions are finally applied, for each strain gauges position, where the resultant applied forces are F = {500, 1500} N. The external surface load that appears in eq. (4) is hence given as fs = F /(2A), being A the area of one of the loaded plates of Fig. 6a. Considering the possible intersections of the defined load and geometrical parameters, then the optimal position is found from a matrix obtained by running 80 FEM analyses combining the different positions and loads reported above.
Fig. 9. Spatial distribution of the y deformations. Top areas from the left are the identified as 1 and 2. Bottom areas from the left are the identified as 4 and 3.
regions. Each line length represents the deformation along y direction and the number of lines increases when higher variations are present. In Fig. 10, the reported lines represent the differences in deformations for strain gauges positioned in different sensitive areas of the pedal while changing the load from 500 N to 1500 N, thus assuming that the higher the slope the higher the strain gauges sensitivity. Each plot shows the behavior for one specific y position while the different lines represent a different x position. The slope of the lines is proportional to the sensitivity, while the difference in slopes represents its variations while moving in different positions. In detail, Fig. 10.a shows the variations for the 8 y-axis positions for the sensitive area 1 of the pedal (the results for the symmetrical area 4 are equivalent), where each line represents a different x positioning of the strain gauges set. A similar behavior is obtained in the sensitive area 2, whose results are shown in Fig. 10.b (the results for the symmetrical area 3 are equivalent). 3.2. Strain gradient evaluation and strain gauges placement
3. Results 3.1. Load-strain results In Fig. 9 the spatial deformation for a load of 1500 N of the pedal bottom surface along Y is shown: this represents the principal directions for strain gauges positioned on the four sensitive
As a further result, the absolute values of the deformation field where evaluated, once more to help in best placing the strain gauges on the final pedal realization. In particular, since the measurement of force signals depends linearly on the differential output from the two strain gauges in each pair, an optimum choice of their placement can be done from processing strain values to
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Fig. 10. Strain gauges output for a) sensitive areas 1 and b) sensitive area 2 of “L shaped” elements, depending on the positions y (different column plots) and x (different lines in each plot) of the strain gauges and the applied loads, as defined in Fig. 8. Strain values are expressed in (m/m).
point out the gradient between adjacent zones along the strain gauge axis: the higher the strain gradient, the higher the gauge pair “output” in that area (higher pedal sensitivity). As already described, the behavior of sensitive areas is not exactly the one of a slender beam hypothesized in eq. (2), even if in the central part of each of those this can be approximated as such. Anyway, minimal variations can be compensated for by a calibration procedure always necessary in the final load cell implementation. The sensitivity at constant load has been studied at 500 N, that represents the minimum load used for dimensioning the pedal body deformations. In Fig. 11.a1 a pedal body scheme is shown with areas 1, 2, 3 and 4 studied by means of the FEM analysis and partitioned into
m × n rectangular regions, with m = 8 and n = 5 and where each region size (i.e. 1.0 mm × 3.0 mm) has been chosen according with the strain gauges matrix dimensions. In each region the strain gradient ε is calculated as the difference between the mean strain values εe and εi associated to the correspondent strain gauges and representing the effect of the Fz components applied to the pedal. In Fig. 11.b1 and 11.b2 numerical results are reported for areas 1 and 2 respectively, due to a 500 N force along z-axis (for the pedal body symmetry, the results for the areas 3 and 4 are equivalent): for areas 1 and 2, the mean strain obtained from average absolute values are ε1 = 5.9 · 10−5 (m/m) and ε2 = 5.3 · 10−5 (m/m), values in agreement with typical ones of a load cell.
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Fig. 11. a1) Pedal body areas 1, 2, 3 and 4 where FEM analysis has been performed. a2) Region of interest for strain gradient evaluation. b1) ε in area 1 under a 500 N load (z-axis). b2) ε in area 2 under a 500 N load (z-axis). Strain values are expressed in (μm/m).
The distribution of ε , at the simulated load of 500 N, for each y position when varying the x one is reported in the boxplot diagrams in Fig. 12, for the sensitive area 1 (a) and 2 (b). This load was chosen in order to obtain the load cell behavior in the minimum excitation conditions, thus allowing understanding better its sensitivity variations while positioning stain gauges pairs in different locations. On the basis of these results an uncertainty analysis can be conducted to evaluate the variations of the obtained measured force when fixing a strain gauge at different positions in the central zone of the sensitive areas. From the tables reported in Fig. 11.b1 and 11.b2, the average values of ε along x (εx ) in the range y = {2 : 3} and along y (ε y ) in the range x = {−1 : 1} can be computed for areas 1-4 (Table 1) and 2-3 (Table 2). Moreover, the variations of εx and ε y per mm, δ(εx ) and δ(ε y ), are computed considering the respective x and y position ranges. From equations (1) and (2), the following can be obtained:
δ F = δ(ε )
EW d
(5)
This can be used to evaluate the error in the force measurement for each μm of misalignment of each strain gauge pair (for aluminum E = 70 GPa). The results for each sensitive area are given in Table 3. 3.3. Prototype implementation and experimental validation On the basis of the illustrated results, the strain gauges pairs have been fixed on a pedal prototype (Fig. 13). The central position with respect to the y direction is the one that is less dependent from the x positioning and at the same time presents good values in terms of sensitivity, as shown in Fig. 10 and Fig. 12. At the same time, a central positioning is the easiest one considering all the practical limitations that affect the installation of small strain gauges (i.e. sensor size, handling, positioning, bonding). In particular, strain gauges were positioned in the following way: a) on sensitive areas 1 and 4 sensors were placed at x = −1 and y = 2;
Fig. 12. ε distributions for a) sensitive area 1 and b) sensitive area 2 under a 500 N load (z-axis) for each y position, as defined in Fig. 8. Strain values are expressed in (m/m).
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Table 1 ε values in the central region of the sensitive areas 1 and 4 under a 500 N load (z-axis), average values along x and y and correspondent δ(εx ) and δ(ε y ) variations per mm. Positions
X = −1 mm
X = 0 mm
X = 1 mm
Average along x
Average δ(εx )/mm
Y = 2 mm Y = 3 mm Averages along y Average δ(ε y )/mm
86 · 10−6 79 · 10−6 82 · 10−6 6.25 · 10−6 /mm
72 · 10−6 72 · 10−6 72 · 10−6
69 · 10−6 71 · 10−6 70 · 10−6
75.7 · 10−6 74 · 10−6
1.7 · 10−6 /mm
AREAS 1 and 4
Table 2 ε values in the central region of the sensitive areas 2 and 3 under a 500 N load (z-axis), average values along x and y and correspondent δ(εx ) and δ(ε y ) variations per mm. Positions
X = −1 mm
X = 0 mm
X = 1 mm
Average along x
Average δ(εx )/mm
Y = 2 mm Y = 3 mm Averages along y Average δ(ε y )/mm
71 · 10−6 61 · 10−6 66 · 10−6 4 · 10−6 /mm
76 · 10−6 60 · 10−6 68 · 10−6
87 · 10−6 61 · 10−6 74 · 10−6
78 · 10−6 60.7 · 10−6
17.3 · 10−6 /mm
AREAS 2 and 3
Table 3 δ F values obtained for misalignment of strain gauges pair in the considered central regions of sensitive areas. AREA
δ F x [N/μm]
δ F y [N/μm]
1–4 2–3
7.9 · 10−3 5 · 10−3
1.7 · 10−3 1.7 · 10−2
Fig. 14. Experimental setup for the load cell-pedal body excitation; A) Stress knob; B) Actuator; C) Reference load cell; D) Stress bracket; E) Load cell-body pedal; F) retaining system. Table 4 Load cell-body pedal output under the Fz component excitation when the Wheatstone bridge is supplied with a V in = 10 V.
Fig. 13. Prototype of the instrumented pedal with strain gauges mounted on the four L-shape areas.
b) on sensitive areas 2 and 3 sensors were placed at x = 1 and y = 2. These parameters represent the ones that provide the best results on the basis of what assessed above. To provide an experimental validation to the numerical simulation results, a preliminary experimental test has been conducted in order to obtain information on the response of the strain gauges to an excitation. A custom-made experimental device, shown in Fig. 14, has been realized to apply the force to the body pedal: acting on the stress knob A, the actuator B applies an excitation on one side of the reference load cell C. This last acts on a rigid stress bracket D that applies the force to the load cell-body pedal positioned in E and retained by the system F. The Wheatstone bridge has been supplied with a V in = 10 V and a Fz component has been applied to the load cell-body pedal in the range {0.05 : 0.55} kN. The results are reported in Table 4. From this table, an average sensitivity of 0.98 mV/kN is obtained, when no additional gain is applied to the Wheatstone bridge output. Considering the equation (2) reported in Section 2.2
load (kN)
output (mV)
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
3.36 3.41 3.46 3.51 3.54 3.6 3.65 3.7 3.75 3.8 3.85
the strain-voltage relation can be expressed as:
ε = ε Area1 + ε Area2 + ε Area3 + ε Area4 =
1 V out kG V in
From experimental results above, εexp . = 0.98 · 10−4 m/m has been measured for Fz = 500 N. On the other hand, from the numerical results obtained by the strain analysis shown in Fig. 11.b1 the estimated range for the strain yields εnum. = and Fig. 11.b2, 0.14 · 10−4 : 4.66 · 10−4 m/m. 4. Discussion From the load-strain results reported in Fig. 9 it is highlighted that the intensity of deformations decreases linearly along the vertical directions of the four arms, generally in agreement with the
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behavior of a slender beam described by eq. (2) and validating the strain gauge general positioning. The presence of 4 screwed holes, used to house the electronics boards, does not significantly affect the linear behavior on the four sensitive areas, even if it can influence the strain gauge pair response when it is positioned in different areas of the corresponding sensitive region. The strain analysis results reported in Fig. 10 gives more details on the load cell behavior when the load is applied in the range {500 : 1500} N. In practical terms what was supposed in the eq. (2), even if it justifies the adopted approach for the implemented parametrical analysis, cannot be strictly applied to this case: the equation indeed represents the behavior of a strain gauges pair when it is fixed on the surface of a simple slender beam to measure the influence of a shear force F . In this simulation, the four analyzed sensitive regions of the pedal cannot be reduced to a simple slender beam but are part of a more complex 3D structure in which the border effect cannot be neglected. Concerning areas 1 and 4 (Fig. 10.a), in both y = 2 and y = 3 positions, a very good sensitivity is obtained, together with a low dependence on the x position and this behavior agrees with the general hypothesis reported above. The latter is a remarkable result, because when strain gauges are fixed, it is very important to obtain a similar behavior to assume that the Wheatstone bridge configuration can work properly. In these two positions (y = 2 and y = 3), the model is minimally affected by the border effects so the considered sensitive region behavior is very similar to the one of a slender beam, where all the lines represented are parallel for each x position. When moving to more extreme positions, the behavior starts to be either dependent from the x position (y = −0.5 to y = 1) or not having a good sensitivity to load (y = −4 to y = 6). For sensitive areas 2 and 3 (Fig. 10.b), for y = 2 and y = 3 once again a very good sensitivity is obtained, together with a low dependence on the x position. In this case, when moving to more extreme positions, the behavior starts to be dependent from the x position for all other y values and in some cases, it presents also an inadequate sensitivity to load (y = −4 to y = 6). The absolute values of the deformation field reported in Fig. 11 show once again that central regions of both areas have a low dependence from x and y. Since the FEM simulation shows a linear behavior of the strain field in the typical range of force application (i.e. from 500 N up to 1500 N), these regions behave similarly at different force levels. Considering ε distributions given in Fig. 12, for both regions, the two central plots representing y = 2 mm and y = 3 mm give the best compromise between a high sensitivity (high average values of ε ) and ease of assembly (low dispersion values with x position variations): in effect, considering the sensitive area 1 (Fig. 12.a) for positions ranging from −0.5 to 3 mm an high sensitivity is obtained, but the high dispersion of values indicates that it is highly influenced by possible mounting errors along the x coordinate, while for positions ranging from 4 to 6 mm a very low sensitivity is obtained, despite a very low dependence from mounting errors along the x coordinate. In the sensitive area 2 (Fig. 12.b) a similar behavior compared to area 1 is highlighted for positions ranging from −0.5 to 3 mm, while for positions ranging from 4 to 6 mm a very low sensitivity is obtained together with a higher dependence from mounting errors along the x coordinate. On the basis of the results obtained by a preliminary uncertainty analysis, it is possible to affirm that the estimated errors in force evaluation when strain gauges pairs are misaligned are not negligible. The results coming from the experimental validation show that the estimated strain is within the range limits obtained from the numerical analysis, and that there is a large variability in terms of strain related to positioning. These aspects confirm that the correct positioning is a crucial point and that an accurate calibration procedure of the load cell
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is always needed to compensate for possible misalignment of the strain gauges. 5. Conclusions The proposed technique represents a suitable method to design new configurations of custom load cells for small loads such as the instrumented pedal described in this paper. The proposed FEM analysis makes it possible to identify those regions that combine high sensitivity (as assented by high average values of strain gradient) and robustness to variations in positioning (quantified by small values of strain gradient variability). The strain gradient is predicted to have maxima that are suitable for strain gauges placement, to improve the measurement system overall sensitivity. Due to the strain gauges configuration and the linear relationship between strain and force on the pedal body, an improvement in strain gradient can be indeed considered as an improvement in device sensitivity. Finally, the method here introduced is suitable for a wide range of load cells where available areas to fix sensors are narrow, and the adopted strain gauges are very small. Anyway, the developed method is going to be tested with direct measurements for different sensors placements: this can give a further validation to the techniques here described. Funding This work did not receive any grant from funding agencies in the public, commercial, or not-for-profit sectors. Author contributions All authors attest that they meet the current International Committee of Medical Journal Editors (ICMJE) criteria for Authorship. Declaration of Competing Interest The authors declare that they have no known competing financial or personal relationships that could be viewed as influencing the work reported in this paper. CRediT authorship contribution statement D. Bibbo: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - original draft, Writing - review & editing. S. Gabriele: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - review & editing. A. Scorza: Data curation, Formal analysis, Investigation, Methodology, Writing - review & editing. M. Schmid: Data curation, Formal analysis, Investigation, Validation, Writing - review & editing. S.A. Sciuto: Data curation, Methodology, Supervision, Writing - review & editing. S. Conforto: Formal analysis, Funding acquisition, Investigation, Project administration, Resources, Supervision, Writing - review & editing. References [1] Patel S, Park H, Bonato P, Chan L, Rodgers M. A review of wearable sensors and systems with application in rehabilitation. J NeuroEng Rehabil 2012;9(1):21. [2] Schmid M, Riganti-Fulginei F, Bernabucci I, Laudani A, Bibbo D, Muscillo R, et al. SVM versus MAP on accelerometer data to distinguish among locomotor activities executed at different speeds. Comput Math Methods Med 2013;2013:343084. [3] Fida B, Bernabucci I, Bibbo D, Conforto S, Proto A, Schmid M. The effect of window length on the classification of dynamic activities through a single accelerometer. In: Proceedings of the IASTED international conference on biomedical engineering; 2014. p. 123–7.
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[4] Bibbo D, Bernabucci I, Scorza A, Orsini F, Sciuto SA, Schmid M. Using IMUs to monitor body kinematics while cycling in different in-field conditions. In: 22nd IMEKO TC4 international symposium and 20th international workshop on ADC modelling and testing 2017: supporting world development through electrical and electronic measurements; 2017. p. 279–82. [5] D’Elia B, Bernabucci I, Bibbo D, Conforto S, D’Alessio T, Sciuto SA, et al. Measuring regularity of fine upper limb movements with a haptic platform for motor learning and rehabilitation 14/23. Lék Tech 2016;46(1):5–12. [6] Brady F. Sports skill classification, gender, and perceptual style. Percept Mot Skills 1995;81(2):611–20. [7] Bieuzen F, Vercruyssen F, Hausswirth C, Brisswalter J. Relationship between strength level and pedal rate. Int J Sports Med 2007;28(7):585–9. [8] Castronovo AM, Conforto S, Schmid M, Bibbo D, D’Alessio T. How to assess performance in cycling: the multivariate nature of influencing factors and related indicators. Front Physiol 2013;4:116. [9] Watson M, Bibbo D, Duffy CR, Riches PE, Conforto S, Macaluso A. Validity and reliability of an alternative method for measuring power output during 6 s all out cycling. J Appl Biomech 2014;30(4):598–603. https://doi.org/10.1123/jab. 2013-0317. PubMed PMID: 24977624. [10] De Marchis C, Castronovo AM, Bibbo D, Schmid M, Conforto S. Muscle synergies are consistent when pedaling under different biomechanical demands. In: Proceedings of the 34th IEEE-EMBS conference; 2012. [11] Cecchini G, et al. Neural networks for muscle forces prediction in cycling. Algorithms 2014;7(4):621–34. [12] Prilutsky BI. Coordination of two- and one-joint muscles: functional consequences and implications for motor control. Mot Control 2000;4(1):1–44.
[13] Soden PD, Adeyefa BA. Force applied to a bicycle during normal cycling. J Biomech 1979;12:527–41. [14] Hull ML, Davis RR. Measurement of pedal loading in bicycling: I. Instrumentation. J Biomech 1981;14(12):843–56. [15] Davis RR, Hull ML. Measurement of pedal loading in bicycling: II. Analysis and results. J Biomech 1981;14(12):857–72. [16] Boyd T, Hull ML, Wootten D. An improved accuracy six-load component pedal dynamometer for cycling. J Biomech 1996;29(8):1105–10. [17] Rowe T, Hull ML, Wang EL. A pedal dynamometer for off-road bicycling. J Biomech Eng 1998;120(1):160–4. [18] Lucchetta M, Petrone N. Progetto di un pedale dinamometrico per l’acquisizione di carichi su biciclette fuoristrada. In: XXVII◦ convegno nazionale AIAS; 1998. [19] Stapelfeldt B, Mornieux G, Oberheim R, Belli A, Gollhofer A. Development and evaluation of a new bicycle instrument for measurements of pedal forces and power output in cycling. Int J Sports Med 2007;28(4):326–32. [20] Bibbo D, Conforto S, Schmid M, D’Alessio T. A wireless integrated system to evaluate efficiency indexes in real time during cycling. In: Proceedings of ECIFMBE IFMBE proceedings; 2008. p. 89–92. [21] Bibbo D, Conforto S, Bernabucci I, Carli M, Schmid M, D’Alessio T. Analysis of different image-based biofeedback models for improving cycling performances. In: Proceedings of SPIE 2012; 2012. Art. no. 829503. [22] Bibbo D, Gabriele S, Scorza A, Schmid M, Sciuto SA, Conforto S. Strain gauges position optimization in designing custom load cells for sport gesture analysis. In: 2018 IEEE 20th international conference on e-health networking, applications and services (Healthcom); 2018. p. 1–6.
Contents lists available at ScienceDirect
IRBM www.elsevier.com/locate/irbm
HEALTHCOM 2018
A Novel Technique to Design and Optimize Performances of Custom Load Cells for Sport Gesture Analysis D. Bibbo a,∗ , S. Gabriele b , A. Scorza a , M. Schmid a , S.A. Sciuto a , S. Conforto a a b
Department of Engineering, Roma Tre University, Rome, Italy Department of Architecture, Roma Tre University, Rome, Italy
h i g h l i g h t s
g r a p h i c a l
a b s t r a c t
• In cycling, estimation of exerted force through force sensors requires high accuracy. • Design of the sensor placement on the pedal can profit from FEM analysis. • Parametric strain-load curves give sensitivity to force and position dependence. • Optimal placement: trade-off between sensitivity and dependence to position changes.
a r t i c l e
i n f o
Article history: Received 13 December 2018 Received in revised form 6 May 2019 Accepted 21 May 2019 Available online 4 June 2019 Keywords: Dynamic analysis Load cells Strain gauges FEM analysis Cycling
a b s t r a c t Background: The assessment of the force exerted during a gesture in human motion analysis can provide direct and indirect information regarding the expended energy, especially during the execution of a sport gesture. In this field, assessment and improvement of the performance can be supported by instrumented devices able to measure and process mechanical quantities. In cycling, strain gauges-based instrumented pedals represent one of the last innovations in the sector, because they can provide data about the power exerted (produced) during training and the pedal efficiency. Optimization of the strain-gauges positioning is thus required to improve accuracy in the exerted force estimation. Methods: A new technique to give a support for evaluating the best compromise between maximum sensitivity and ease of assembly was developed in the present work, based on a Finite Element Model (FEM) and a parametric analysis of the strain field at different sensor placements. Optimal positions were identified as those combining high sensitivity and low dependence from positioning inaccuracies. Results: Parametric strain-load trends obtained from the developed model show a linear behavior of strain gauges pairs and confirm that there is a good sensitivity of the adopted sensors if they are mounted in handy positions of the developed load cell. Discussion: The conducted analysis enables to calculate the sensitivity of the load cell to the exerted forces, and evaluates its dependence to the positioning of strain gauges, and makes it possible to appropriately choose strain gauges positioning in areas where border effects are minimized. The strain distributions obtained by the FEM analysis in the presented load cells gives useful indications for all the situations where small strain gauges are requested to be mounted on a reduced offered area. © 2019 AGBM. Published by Elsevier Masson SAS. All rights reserved.
1. Introduction
*
Corresponding author. E-mail address: [email protected] (D. Bibbo).
https://doi.org/10.1016/j.irbm.2019.05.005 1959-0318/© 2019 AGBM. Published by Elsevier Masson SAS. All rights reserved.
Sport science in the last decades has taken great advantage from the use of electronic devices dedicated both to athletes’ ges-
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ture monitoring and to the provision of real-time feedback information, with the aim of improving performance. The information obtained by measuring human motion parameters can be used to assess the correct execution of motor tasks that compose the gesture itself or to recognize dynamic activities [1–5]. One of the main classifications of a sport gesture describes it as either an “open skill” sport discipline, characterized by a free and unconstrained strategy expressed by the athlete according to the specific situation (i.e. football, basket etc.), or as a “closed skill” one, characterized by the repetition as accurate as possible of a well-known gesture and by its almost automatic execution [6], such as in rowing, archery or cycling. In cycling the athlete continuously repeats the act of pedaling that implies a dynamic interaction with the pedal and can be well identified, quantified and interpreted. In general, the study of the cycling biomechanics can help to evaluate how the athlete executes the required motor task, especially when the performance can be assessed on the basis of objective parameters [7,8]. One of the most reliable methodologies widely used in this context is the pedaling power evaluation: this quantity can be assessed using different techniques [9], or on the basis of the estimation the muscle activity during the task [10]. During cycling, many factors contribute to the total resistance that must be overcome for the advancement of the bicycle, such as aerodynamic ones, mechanical frictions or rolling resistances, that can be equivalently schematized as a total resistant torque applied to the wheel. At constant pedaling, the forces applied to the pedal must win this resistant torque, thus the analysis of pedaling dynamics can give important information on the way such forces are applied and on their intensity. One important application of pedal use, described in some literature works, consists of the measurement of the external forces exerted on the pedal for predicting muscle force patterns, using an inverse dynamics approach [11,12]. Some of the most important proposals of the last decades are based on the measure of the forces applied to the pedal, using custom developed instrumented bicycle pedals. These solutions, useful to provide the dynamic information related to the foot-pedal interaction, are based on various technologies, aiming to obtain good performances in terms of accuracy and reliability. Soden and co-workers, in 1979 [13], presented one of the first proposals that demonstrated the feasibility of using such pedals. The main goal of the work was to obtain a tool for the design and the structural dimensioning of the bicycle frames. In doing this, authors proved, with a relative compact instrument, the possibility of measuring forces applied to the pedal, using different channels for each component of the dynamic measurement. After this, successive studies dealt with the development of a multicomponent instrumented pedal to measure kinetics (i.e. the threedimensional force and torque vectors in a reference system fixed to the pedal) and kinematics (i.e. the angle between the crank and the pedal) during cycling. It was assessed and demonstrated that to completely describe the cycling biomechanics these measurements were necessary, also for the calculation of the pedaling effective force [14,15], that causes bicycle progression. Successive works enlarged the knowledge on the pedaling technique [16,17] even if the described solutions were not useful for applications out of the laboratory environment. The first solution to overcome the described limits was proposed in 1998 [18] for off-road bicycles. A new instrumented pedal with dimensions and weight closer to a normal one, and so compatible with in-field applications, was presented, even if with some limitations. The acquisition system was compact and the load cell well designed, so allowing accurate measurements of the force components in agreement with the authors’ original aim relating to the stress analysis of the bicycle frame. This solution was affected by a pair of drawbacks preventing the transformation of this proposal into a com-
mercial device: i) wired connection of the instrumented pedal to the acquisition system; ii) crank modified to fit the instrumented pedal. Also, more recent proposals [19] imply non-negligible modifications on the bike, thus affecting the gesture execution. To be consistent with the original crankset geometry, the crank has to be shortened, thus the measuring device is not compliant with standard cranksets and can be used only in combination with tools providing different crank lengths. In the last years, among the commercial devices useful to evaluate the power exerted while pedaling, the Powermeter (SRM GMBH, Germany, EU) was introduced. Even if it represented a small revolution among sports bicycle users, it presents a main limit: this system provides only the resultant torque from which it is not possible to obtain the two contributions that each leg provides during cycling. To overcome these limits, a new system for torque and force measurements, based on a different general concept, was designed and developed by our group [20,21]. The design of such a system considers a new concept for the instrumented pedal body as well as its manufacturing process. One of the most important aspects in the design and realization of this system is the optimization of sensors dimensioning and placement, aiming to obtain the best tradeoff between bending behavior in the elastic field, that is related to the instrument sensitivity, and mechanical resistance. To this aim, and on the basis of a previous study by our group [22], in this paper a simulation of the strain field for different sensors positions was conducted. The results of this study can help support the evaluations of such kind of sensors design in order to achieve the best compromise between ease of assembly and maximum sensitivity. To this aim, after some theoretical considerations on sensors settings and configuration, numerical results from a 3D Finite Element Model (FEM) simulation are shown and discussed. The innovation consists also in a multi parametric 3D modelling and analysis, in which it is possible to variate the dimension of the load cell and of the strain gauges, together with the different positioning of those on the designed structure. The proposed method can be easily applied to a wide range of force sensors, especially the ones where the available area to fix sensors is reduced and strain gauges adopted are very small. The choice of an optimal position can guarantee a reduction of mounting errors, thus increasing the quality of the final product. 2. Materials and methods 2.1. Instrumented pedal mechanical design In order to reconstruct the effective component of force applied by the cyclist, which is the one orthogonal to the crank [16] and gives the necessary torque to move the bicycle, a novel instrumented pedal was designed. To this aim the necessary requirements are the possibility of measuring the three components of the force and the angle between the pedal and the pedal crank. Since in cycling even minimal variations to each bicycle component can affect the athlete’s performance, the pedal was designed with mechanical and geometrical features to be compliant, in terms of shape, weight and dimensions, to a commercial one. The pedal body, aiming at both weight and size optimization, was proposed and realized in a single block of aluminum alloy, and its weight, including all the complementary accessories, is 200 g. The shape allows a simple die-casting production because it does not present undercuts in its mechanical design. Moreover, the pedal body has some specific sensitive areas whose deformation can be associated with the load applied to the pedal by a cycling shoe commercial cleat. The central axis of the pedal used for the connection
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Fig. 1. Body of the designed instrumented pedal.
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Fig. 3. Effect on the lower parts of the 4 “L shape” elements while a Fz components is applied to the pedal. Sensitive areas 1 to 4 are highlighted.
Fig. 2. “L-shape” elements for the strain gauges fixing. The different sets are positioned in yellow, green and red highlighted areas for the measure of Fx, Fy and Fz respectively. Two yellow and green areas are not visible but located symmetrically to the visible ones with respect to the yz and xz planes. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.) Fig. 4. Strain gauge positioning for the Fz component measurement.
with the crank, as well as the spring mechanism for the cleat retain system, was taken from a commercial pedal solution (Shimano SPD-SL). The electronic circuits for conditioning, acquiring and transmitting signals from the force sensors are enclosed in a specific carter fixed to the pedal body. In the pedal design, shown in Fig. 1, the main concept has been to transmit the force flow from the shoes contact point to the crank via four sensitive and sensorized elements: the force exerted by the cyclist is applied on the upper load plate (1) that is fixed to the two lateral zones of the pedal body (2). Then the force is transmitted on four “L-shape” elements (3) on which the strain gauges are placed (see also Fig. 2). With reference to Fig. 1, these elements are connected to a central housing (4) in which the pedal shaft (along y axis), that connects the pedal to the crank, is fixed using bearings. It is important to highlight that elements 1 and 4 are not in contact so the force flow is transmitted only via the elements 3. On the opposite side of the threaded axis, a digital encoder is positioned (5), to measure the pedal-crank angle. The innovative pedal design therefore allows measuring the desired components presenting a compact and light shape and simplifies its manufacturing process. 2.2. Strain gauge disposition and assembly Under the action of a force applied on the pedal load plane, the “L shape” elements are deformed, under the hypothesis of an elastic behavior, in order to transduce the stress in strain. Consequently, the force effect that can be measured comes from a deformation of these elements, in different directions and intensity depending on the force components, schematized along the 3 axes (x, y, z) represented in Fig. 1. To evaluate deformations while applying force, 3 different sets of strain gauges (8 for each component, 24 total) are necessary to monitor the deformation of the “L-shape” elements, and are placed as shown in Fig. 2. Each set is assumed to measure the same kind of deformation, because the 3 force components act as a shear force on different parts of the “L-shape” element. These assumptions allow measuring the three components minimizing the cross
talk between channels: for example, considering the strain gauges set used to monitor the Fz component, this channel will have a zero output when Fx and Fy are applied on the load plane. The single strain gauge electrical resistance is in general proportional to its deformation, so the force applied to the pedal can be measured by assembling strain gauges in Wheatstone bridge configurations. In this way it is possible to assume that F = A × V out , with F representing the applied force, V out the bridge voltage output and A the coefficient that gives the linear proportionality. In this application three different sets of strain gauges are used to measure the three force components along the respective orthogonal axes. These sets are consequently assembled in 3 independent Wheatstone bridge circuits. The Fx, Fy and Fz force components can be obtained considering the superposition principle on each of the “L-shape” pedal elements: every part of each element, under the action of a single force component, has a behavior similar to a beam structure subject to a shear force. For example, when the Fz component is applied to the pedal, the situation can be considered equivalent as four components (Fz1 , Fz2 , Fz3 , Fz4 ), whose sum gives Fz, are applied to the lower parts of the 4 “L shape” elements (Fig. 3). The resulting deformation, as a first approximation, results as a consequence of the bending action of each (Fz1 , Fz2 , Fz3 , Fz4 ) component only. In this condition, a simplified model can be used to describe how to measure each Fzn shear component: the single element can be considered as a fixed beam, 2 strain gauges can be mounted in the external position “e” and internal position “i”, as shown in Fig. 4, to measure the resulting normal stresses. To do this, at first it is necessary to assume a linear elastic behavior of the material: under these conditions the stress/strain relation is given M by the σ = E ε = Wb . In a generic beam section, the deformation is consequently function of the force F , according to the equations:
ε=
Mb EW
where:
=F
1 EW
a
(1)
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Fig. 5. Wheatstone bridge configuration for the Fz component measurement.
• • • •
M b : the bending moment in the generic section n; a: the force arm; E: the Young’s modulus of the material; W : the modulus of the resistance to the bending.
Considering a pair of strain gauges “e” and “i” placed on one of the sensing elements (Fig. 4), with respective electrical resistance R e and R i and assembled in a Wheatstone bridge configuration (Fig. 5), the output signal is:
V out V in V out V in
=k =
Re Re
kG EW
−
Ri
Ri
= kG (εe − εi ) =
kG EW
(ae − ai ) F
dF
(2)
where:
• G: the Gauge Factor; • d: distance between the strain gauges; • k: constant of proportionality.
Fig. 6. 3D Geometry with a) loaded plates and b) restrained internal surface highlighted.
With this configuration, the measure of F is theoretically independent from its application point on the beam. Of course, this specific aspect is sensitive to the boundary conditions. On the basis of these considerations, 8 strain gauges can be fixed on the lowest part of the pedal as shown in Fig. 4 and assembled as shown in Fig. 5. As initial hypothesis a pair consists of a single matrix composed by 2 strain gauges, whose size is 1.5 × 1 mm. The 2 strain gauges are distant 0.5 mm so the matrix dimensions are 3.5 × 1 mm. Considering a V in input, the voltage output V out of the circuit is given by:
V out V in
=k +
1 Z e 1 Ze
4 Z e 4 Ze
−
1 Z i
−
4 Z i
1 Zi 4 Zi
+
2 Z e 2 Ze
−
2 Z i 2 Zi
+
3 Z e 3 Ze
−
3 Z i 3 Zi (3)
with {1Ze, 1Zi, 2Ze, 2Zi, 3Ze, 3Zi, 4Ze, 4Zi} the strain gauges electric resistance values and {1Ze, 1Zi, 2Ze, 2Zi, 3Ze, 3Zi, 4Ze, 4Zi} their variations, while Fz is applied and k a constant. The other two force components Fx and Fy can be measured in an equivalent way, so the analysis conducted in this paper for one of the components (Fz) can be repeated in the same way for the others. 2.3. Structural analysis To evaluate the strain values, in particular those close to the zones interested by the strain gauges position, a parametric mechanical analysis of the pedal was conducted. From a quantitative point of view, the analysis gives an estimation of the maximum strains experienced by the pedal and allows for verifying the consistency with the strain gauges sensitivities. Moreover, parametric
calculations help to infer the optimal positioning of the necessary sensors. A 3D FEM of the pedal has been implemented using COMSOL Multiphysics. In Fig. 6 the geometry of the model is shown, where the loaded plates (see also zones 2, Fig. 1) are highlighted. The pedal positioning with respect to the foot position during cycling can be simulated in the best way also considering some boundary conditions (BCs), given in half of the inner hollow surface of the pedal (see Fig. 6b). In this analysis the foot pressure is assumed normal to the loaded plates along the Z axis (Fig. 6a). All the geometrical details led to a very complex 3D mesh with a high number of edges: the complete mesh is depicted in Fig. 7 and consists of 32851 domain elements, 10390 boundary elements, and 2002 edge elements, the total number of degrees of freedom solved for is 154788. The provided numbers give an idea of the model complexity. In particular the domain elements are, in this case, tetrahedral objects where a physical problem to be solved can be attached. In the present case the linear static equilibrium equations are solved over the 3D domain ,
di v (S) = 0 in , S · n = f s on L , u = u on R
(4)
where S is the Cauchy stress tensor, f s are the surface loads applied on L and u are the values of the displacement boundary conditions applied on R . The strain gauges are simulated considering that the total strain of the sensor acts as the underneath surface, so the behavior can be considered to be the same. With these considerations, strain gauges can be simulated on the model as a pair of 2D rectangular patches, as in Fig. 7. To simulate their deformation an average operator is then applied to each of the patches, thus giving the mean value of the strain measure ε22 through the longest side of the patch. A proper fine meshing of the area around the patches (see
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Fig. 7. 3D mesh and strain gauge position simulation.
Fig. 8. Strain gauge positioning along vertical (y) and horizontal (x) directions. Positions are expressed in mm.
Fig. 7) is applied in order to improve the accuracy in the calculated average value of the strain. 2.4. Parametric technique for the strain gauge position analysis A parametric analysis has been conducted to study the position of the strain gauges. From a “zero” initial position that is depicted in Fig. 8, both translations along the vertical (y) and horizontal (x) directions are applied, as to obtain a matrix of 8 by 5 different strain gauges positions. The vectors of the translation parameters yp and xp, for the vertical and the horizontal positions respectively, are given in the following:
yp = {−0.5, 0, 1, 2, 3, 4, 5, 6} [mm] xp = {−2, −1, 0, 1, 2} [mm] Two different load conditions are finally applied, for each strain gauges position, where the resultant applied forces are F = {500, 1500} N. The external surface load that appears in eq. (4) is hence given as fs = F /(2A), being A the area of one of the loaded plates of Fig. 6a. Considering the possible intersections of the defined load and geometrical parameters, then the optimal position is found from a matrix obtained by running 80 FEM analyses combining the different positions and loads reported above.
Fig. 9. Spatial distribution of the y deformations. Top areas from the left are the identified as 1 and 2. Bottom areas from the left are the identified as 4 and 3.
regions. Each line length represents the deformation along y direction and the number of lines increases when higher variations are present. In Fig. 10, the reported lines represent the differences in deformations for strain gauges positioned in different sensitive areas of the pedal while changing the load from 500 N to 1500 N, thus assuming that the higher the slope the higher the strain gauges sensitivity. Each plot shows the behavior for one specific y position while the different lines represent a different x position. The slope of the lines is proportional to the sensitivity, while the difference in slopes represents its variations while moving in different positions. In detail, Fig. 10.a shows the variations for the 8 y-axis positions for the sensitive area 1 of the pedal (the results for the symmetrical area 4 are equivalent), where each line represents a different x positioning of the strain gauges set. A similar behavior is obtained in the sensitive area 2, whose results are shown in Fig. 10.b (the results for the symmetrical area 3 are equivalent). 3.2. Strain gradient evaluation and strain gauges placement
3. Results 3.1. Load-strain results In Fig. 9 the spatial deformation for a load of 1500 N of the pedal bottom surface along Y is shown: this represents the principal directions for strain gauges positioned on the four sensitive
As a further result, the absolute values of the deformation field where evaluated, once more to help in best placing the strain gauges on the final pedal realization. In particular, since the measurement of force signals depends linearly on the differential output from the two strain gauges in each pair, an optimum choice of their placement can be done from processing strain values to
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Fig. 10. Strain gauges output for a) sensitive areas 1 and b) sensitive area 2 of “L shaped” elements, depending on the positions y (different column plots) and x (different lines in each plot) of the strain gauges and the applied loads, as defined in Fig. 8. Strain values are expressed in (m/m).
point out the gradient between adjacent zones along the strain gauge axis: the higher the strain gradient, the higher the gauge pair “output” in that area (higher pedal sensitivity). As already described, the behavior of sensitive areas is not exactly the one of a slender beam hypothesized in eq. (2), even if in the central part of each of those this can be approximated as such. Anyway, minimal variations can be compensated for by a calibration procedure always necessary in the final load cell implementation. The sensitivity at constant load has been studied at 500 N, that represents the minimum load used for dimensioning the pedal body deformations. In Fig. 11.a1 a pedal body scheme is shown with areas 1, 2, 3 and 4 studied by means of the FEM analysis and partitioned into
m × n rectangular regions, with m = 8 and n = 5 and where each region size (i.e. 1.0 mm × 3.0 mm) has been chosen according with the strain gauges matrix dimensions. In each region the strain gradient ε is calculated as the difference between the mean strain values εe and εi associated to the correspondent strain gauges and representing the effect of the Fz components applied to the pedal. In Fig. 11.b1 and 11.b2 numerical results are reported for areas 1 and 2 respectively, due to a 500 N force along z-axis (for the pedal body symmetry, the results for the areas 3 and 4 are equivalent): for areas 1 and 2, the mean strain obtained from average absolute values are ε1 = 5.9 · 10−5 (m/m) and ε2 = 5.3 · 10−5 (m/m), values in agreement with typical ones of a load cell.
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Fig. 11. a1) Pedal body areas 1, 2, 3 and 4 where FEM analysis has been performed. a2) Region of interest for strain gradient evaluation. b1) ε in area 1 under a 500 N load (z-axis). b2) ε in area 2 under a 500 N load (z-axis). Strain values are expressed in (μm/m).
The distribution of ε , at the simulated load of 500 N, for each y position when varying the x one is reported in the boxplot diagrams in Fig. 12, for the sensitive area 1 (a) and 2 (b). This load was chosen in order to obtain the load cell behavior in the minimum excitation conditions, thus allowing understanding better its sensitivity variations while positioning stain gauges pairs in different locations. On the basis of these results an uncertainty analysis can be conducted to evaluate the variations of the obtained measured force when fixing a strain gauge at different positions in the central zone of the sensitive areas. From the tables reported in Fig. 11.b1 and 11.b2, the average values of ε along x (εx ) in the range y = {2 : 3} and along y (ε y ) in the range x = {−1 : 1} can be computed for areas 1-4 (Table 1) and 2-3 (Table 2). Moreover, the variations of εx and ε y per mm, δ(εx ) and δ(ε y ), are computed considering the respective x and y position ranges. From equations (1) and (2), the following can be obtained:
δ F = δ(ε )
EW d
(5)
This can be used to evaluate the error in the force measurement for each μm of misalignment of each strain gauge pair (for aluminum E = 70 GPa). The results for each sensitive area are given in Table 3. 3.3. Prototype implementation and experimental validation On the basis of the illustrated results, the strain gauges pairs have been fixed on a pedal prototype (Fig. 13). The central position with respect to the y direction is the one that is less dependent from the x positioning and at the same time presents good values in terms of sensitivity, as shown in Fig. 10 and Fig. 12. At the same time, a central positioning is the easiest one considering all the practical limitations that affect the installation of small strain gauges (i.e. sensor size, handling, positioning, bonding). In particular, strain gauges were positioned in the following way: a) on sensitive areas 1 and 4 sensors were placed at x = −1 and y = 2;
Fig. 12. ε distributions for a) sensitive area 1 and b) sensitive area 2 under a 500 N load (z-axis) for each y position, as defined in Fig. 8. Strain values are expressed in (m/m).
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Table 1 ε values in the central region of the sensitive areas 1 and 4 under a 500 N load (z-axis), average values along x and y and correspondent δ(εx ) and δ(ε y ) variations per mm. Positions
X = −1 mm
X = 0 mm
X = 1 mm
Average along x
Average δ(εx )/mm
Y = 2 mm Y = 3 mm Averages along y Average δ(ε y )/mm
86 · 10−6 79 · 10−6 82 · 10−6 6.25 · 10−6 /mm
72 · 10−6 72 · 10−6 72 · 10−6
69 · 10−6 71 · 10−6 70 · 10−6
75.7 · 10−6 74 · 10−6
1.7 · 10−6 /mm
AREAS 1 and 4
Table 2 ε values in the central region of the sensitive areas 2 and 3 under a 500 N load (z-axis), average values along x and y and correspondent δ(εx ) and δ(ε y ) variations per mm. Positions
X = −1 mm
X = 0 mm
X = 1 mm
Average along x
Average δ(εx )/mm
Y = 2 mm Y = 3 mm Averages along y Average δ(ε y )/mm
71 · 10−6 61 · 10−6 66 · 10−6 4 · 10−6 /mm
76 · 10−6 60 · 10−6 68 · 10−6
87 · 10−6 61 · 10−6 74 · 10−6
78 · 10−6 60.7 · 10−6
17.3 · 10−6 /mm
AREAS 2 and 3
Table 3 δ F values obtained for misalignment of strain gauges pair in the considered central regions of sensitive areas. AREA
δ F x [N/μm]
δ F y [N/μm]
1–4 2–3
7.9 · 10−3 5 · 10−3
1.7 · 10−3 1.7 · 10−2
Fig. 14. Experimental setup for the load cell-pedal body excitation; A) Stress knob; B) Actuator; C) Reference load cell; D) Stress bracket; E) Load cell-body pedal; F) retaining system. Table 4 Load cell-body pedal output under the Fz component excitation when the Wheatstone bridge is supplied with a V in = 10 V.
Fig. 13. Prototype of the instrumented pedal with strain gauges mounted on the four L-shape areas.
b) on sensitive areas 2 and 3 sensors were placed at x = 1 and y = 2. These parameters represent the ones that provide the best results on the basis of what assessed above. To provide an experimental validation to the numerical simulation results, a preliminary experimental test has been conducted in order to obtain information on the response of the strain gauges to an excitation. A custom-made experimental device, shown in Fig. 14, has been realized to apply the force to the body pedal: acting on the stress knob A, the actuator B applies an excitation on one side of the reference load cell C. This last acts on a rigid stress bracket D that applies the force to the load cell-body pedal positioned in E and retained by the system F. The Wheatstone bridge has been supplied with a V in = 10 V and a Fz component has been applied to the load cell-body pedal in the range {0.05 : 0.55} kN. The results are reported in Table 4. From this table, an average sensitivity of 0.98 mV/kN is obtained, when no additional gain is applied to the Wheatstone bridge output. Considering the equation (2) reported in Section 2.2
load (kN)
output (mV)
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
3.36 3.41 3.46 3.51 3.54 3.6 3.65 3.7 3.75 3.8 3.85
the strain-voltage relation can be expressed as:
ε = ε Area1 + ε Area2 + ε Area3 + ε Area4 =
1 V out kG V in
From experimental results above, εexp . = 0.98 · 10−4 m/m has been measured for Fz = 500 N. On the other hand, from the numerical results obtained by the strain analysis shown in Fig. 11.b1 the estimated range for the strain yields εnum. = and Fig. 11.b2, 0.14 · 10−4 : 4.66 · 10−4 m/m. 4. Discussion From the load-strain results reported in Fig. 9 it is highlighted that the intensity of deformations decreases linearly along the vertical directions of the four arms, generally in agreement with the
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behavior of a slender beam described by eq. (2) and validating the strain gauge general positioning. The presence of 4 screwed holes, used to house the electronics boards, does not significantly affect the linear behavior on the four sensitive areas, even if it can influence the strain gauge pair response when it is positioned in different areas of the corresponding sensitive region. The strain analysis results reported in Fig. 10 gives more details on the load cell behavior when the load is applied in the range {500 : 1500} N. In practical terms what was supposed in the eq. (2), even if it justifies the adopted approach for the implemented parametrical analysis, cannot be strictly applied to this case: the equation indeed represents the behavior of a strain gauges pair when it is fixed on the surface of a simple slender beam to measure the influence of a shear force F . In this simulation, the four analyzed sensitive regions of the pedal cannot be reduced to a simple slender beam but are part of a more complex 3D structure in which the border effect cannot be neglected. Concerning areas 1 and 4 (Fig. 10.a), in both y = 2 and y = 3 positions, a very good sensitivity is obtained, together with a low dependence on the x position and this behavior agrees with the general hypothesis reported above. The latter is a remarkable result, because when strain gauges are fixed, it is very important to obtain a similar behavior to assume that the Wheatstone bridge configuration can work properly. In these two positions (y = 2 and y = 3), the model is minimally affected by the border effects so the considered sensitive region behavior is very similar to the one of a slender beam, where all the lines represented are parallel for each x position. When moving to more extreme positions, the behavior starts to be either dependent from the x position (y = −0.5 to y = 1) or not having a good sensitivity to load (y = −4 to y = 6). For sensitive areas 2 and 3 (Fig. 10.b), for y = 2 and y = 3 once again a very good sensitivity is obtained, together with a low dependence on the x position. In this case, when moving to more extreme positions, the behavior starts to be dependent from the x position for all other y values and in some cases, it presents also an inadequate sensitivity to load (y = −4 to y = 6). The absolute values of the deformation field reported in Fig. 11 show once again that central regions of both areas have a low dependence from x and y. Since the FEM simulation shows a linear behavior of the strain field in the typical range of force application (i.e. from 500 N up to 1500 N), these regions behave similarly at different force levels. Considering ε distributions given in Fig. 12, for both regions, the two central plots representing y = 2 mm and y = 3 mm give the best compromise between a high sensitivity (high average values of ε ) and ease of assembly (low dispersion values with x position variations): in effect, considering the sensitive area 1 (Fig. 12.a) for positions ranging from −0.5 to 3 mm an high sensitivity is obtained, but the high dispersion of values indicates that it is highly influenced by possible mounting errors along the x coordinate, while for positions ranging from 4 to 6 mm a very low sensitivity is obtained, despite a very low dependence from mounting errors along the x coordinate. In the sensitive area 2 (Fig. 12.b) a similar behavior compared to area 1 is highlighted for positions ranging from −0.5 to 3 mm, while for positions ranging from 4 to 6 mm a very low sensitivity is obtained together with a higher dependence from mounting errors along the x coordinate. On the basis of the results obtained by a preliminary uncertainty analysis, it is possible to affirm that the estimated errors in force evaluation when strain gauges pairs are misaligned are not negligible. The results coming from the experimental validation show that the estimated strain is within the range limits obtained from the numerical analysis, and that there is a large variability in terms of strain related to positioning. These aspects confirm that the correct positioning is a crucial point and that an accurate calibration procedure of the load cell
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is always needed to compensate for possible misalignment of the strain gauges. 5. Conclusions The proposed technique represents a suitable method to design new configurations of custom load cells for small loads such as the instrumented pedal described in this paper. The proposed FEM analysis makes it possible to identify those regions that combine high sensitivity (as assented by high average values of strain gradient) and robustness to variations in positioning (quantified by small values of strain gradient variability). The strain gradient is predicted to have maxima that are suitable for strain gauges placement, to improve the measurement system overall sensitivity. Due to the strain gauges configuration and the linear relationship between strain and force on the pedal body, an improvement in strain gradient can be indeed considered as an improvement in device sensitivity. Finally, the method here introduced is suitable for a wide range of load cells where available areas to fix sensors are narrow, and the adopted strain gauges are very small. Anyway, the developed method is going to be tested with direct measurements for different sensors placements: this can give a further validation to the techniques here described. Funding This work did not receive any grant from funding agencies in the public, commercial, or not-for-profit sectors. Author contributions All authors attest that they meet the current International Committee of Medical Journal Editors (ICMJE) criteria for Authorship. Declaration of Competing Interest The authors declare that they have no known competing financial or personal relationships that could be viewed as influencing the work reported in this paper. CRediT authorship contribution statement D. Bibbo: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - original draft, Writing - review & editing. S. Gabriele: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - review & editing. A. Scorza: Data curation, Formal analysis, Investigation, Methodology, Writing - review & editing. M. Schmid: Data curation, Formal analysis, Investigation, Validation, Writing - review & editing. S.A. Sciuto: Data curation, Methodology, Supervision, Writing - review & editing. S. Conforto: Formal analysis, Funding acquisition, Investigation, Project administration, Resources, Supervision, Writing - review & editing. References [1] Patel S, Park H, Bonato P, Chan L, Rodgers M. A review of wearable sensors and systems with application in rehabilitation. J NeuroEng Rehabil 2012;9(1):21. [2] Schmid M, Riganti-Fulginei F, Bernabucci I, Laudani A, Bibbo D, Muscillo R, et al. SVM versus MAP on accelerometer data to distinguish among locomotor activities executed at different speeds. Comput Math Methods Med 2013;2013:343084. [3] Fida B, Bernabucci I, Bibbo D, Conforto S, Proto A, Schmid M. The effect of window length on the classification of dynamic activities through a single accelerometer. In: Proceedings of the IASTED international conference on biomedical engineering; 2014. p. 123–7.
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